This invention relates in general to Multi Input Multi Output (MIMO) 2-way Wireless Communication Systems. More specifically, this invention is related to MIMO 2-way Wireless Communication Systems where Multiple Antenna Arrays (MAA) are used in some of the system communication devices, where the propagation Channel Matrix is random, where Channel Information is available at both the Transmitter and Receiving sides, and where said propagation Channel Matrix information is imperfectly estimated.
During recent years Multi Input Multi Output (MIMO) schemes were proposed for Wireless Communication Systems whereby some of the system communication devices include Multiple Antenna Arrays (MAA) and associated transmission and reception circuitry. MIMO systems, when operated in richly scattering channels (such as typical urban and indoor channels in conjunction with properly designed antenna arrays) may exhibit antenna array gain, space diversity gain (and thus Extended Range), and, in certain cases, the ability to effectively multiply the overall data rate transferred thru the channel by means of splitting the data stream into several sub-streams, each transferred through one of a set of separate propagation channel ‘modes’ (and thus achieving Extended Rate). Note that while the term Extended Capacity could be used instead of both Extended Range/Rate (since range can be usually traded off by rate and vice-versa) we prefer the latter distinction along this text to distinguish between the ‘conventional’ array/diversity gains on one hand, and the ability to transmit several data sub-streams in parallel, which may be achieved only when the 2 communicating sides include an MAA, on the other.
In some of these schemes, relevant to this invention, the propagation complex Channel transfer Matrix H of R×L elements is estimated at one or both of the receiving sides during a Training Stage, where L and R denote the number of antennas and corresponding circuitry in the Left and Right side devices respectively (and usually L and/or R>1). A standard Singular Value Decomposition operation (usually denoted SVD in elementary matrix algebra texts) is subsequently conducted on this estimated channel matrix so that H=U D V′ where U and V are R×R and L×L unitary matrices whose columns are the eigen-vectors of H H′ and H′H respectively, D is an R×L diagonal matrix, and ( )′ denotes the matrix conjugate transpose operator.
The diagonal elements Di of the matrix D, known as the Singular Values of H, are the (non-negative, real) square roots of the eigen-values of H′ H, and, as such, are proportional to the gain of each of the channel H fore-mentioned parallel transmission ‘modes’. In some of these same MAA schemes another diagonal real Power Allocation Matrix A is applied at the transmitting side to the data symbols vector s, prior to any other processing so that equal power is allocated to each of the user data sub-streams, or (other times) alternatively so that the data sub-stream components associated to channel ‘modes’ with more favorable gain (i.e. greater magnitude Singular Values) are allocated more power following the ‘water pouring’ algorithm described in e.g. [9], and vice-versa, and so that the overall transmitted power is constrained.
At the end of this Training Stage, information related to this channel matrix H (or to relevant parts of its SVD decomposition) resides at both Left and Right sides, the Transmitting side (say Left) applies the unitary complex matrix V as a transmission weight upon the transmitted vector sequence, and the Receiving side (say Right) applies the unitary complex matrix U′ as its reception weight upon the received vector.
Summarizing in matrix notation the signal processing executed in some of these fore-mentioned schemes as described above, denoting by s the (usually complex) source data sub-stream vector (of dimension M≦min {L, R}), by x the complex base-band representation of the transmitted signal vector (of dimension L, assuming without loss of generality that Left is the Transmitting side), by y the complex base-band representation of the received signal vector (of dimension R, assuming Right is the Receiving side), by r the recovered data sub-stream complex vector, and neglecting the receiving circuitry (and possibly interference) noise, we have:x=VAs y=Hx=(UDV′)x=UDV′VAs r=U′y=(U′U)D(V′V)A s=DAs  Eq. 1where we have exploited the fact that both U and V are unitary (U′ U=I where I is the Identity matrix, etc.). Hence, since both D and A are diagonal, each element of r is a (scaled) version of a corresponding element of s, as required for perfect and simple data recovery.
Other MAA schemes, similar in purpose and nature, were also described (e.g. [4]) whereby the actual processing is conducted at the Frequency Domain, rather than the Time Domain, thus allowing optimization of the said Weighting Matrices to each useful bandwidth slot, for example each OFDM sub-carrier, as would be required in the presence of Frequency Selective Fading propagation channels.
Still other MIMO schemes, less relevant to the present invention but also similar in purpose were described (e.g. [1], [2]) whereby no Channel Matrix information is required at the transmitting side, whereby the propagation complex Channel transfer Matrix H of R×L elements is assumed to be known only at the Receiving side, and whereby the received data recovery is performed by means of applying specific solution methods to the Equation y=H x where y, H and x are as defined above.
It is generally implicitly assumed in these schemes that the propagation channel matrix H is perfectly estimated during a so called Channel Training (or Acquisition) Stage so that perfect information about the channel is available at the end of said Training Stage at the receiving and, (if required) the transmitting sides. It is also generally assumed that the channel matrix H elements are complex random variables and, as such, that the Singular Values of H are random variables as well. The processing nature of the for-mentioned Channel Matrix Acquisition Stage is generally ignored, in contrast with non-MIMO wireless communication systems where (Scalar) Channel initial estimation methods have been extensively studied and applied (e.g. [5]).
The assumption concerning perfect channel estimation is generally not valid. Typical propagation channels and receiving circuitry are noisy and the channel Training Stage is usually time limited. Since the channel matrix estimation error depends on both the channel measurements Signal to Noise Ratio (SNR) and on the number of measurements, the estimated result, denoted Hn is usually different from the actual channel matrix H, that is Hn=H+dH where dH is the estimation error. The Singular Value Decomposition of Hn is Un Dn Vn′ where, again, the subscript n denotes the noisy version of the actual corresponding counterparts U D V′ which were described above. Replacing in Equation 1 these noisy versions we get:r=Un′y=(Un′U)D(V′Vn)As  Eq. 2where we do not get the perfect signal recovery as described in Equation 1 since Un′ U and V′ Vn do not equal the Identity matrix anymore, so that the recovered data sub-stream elements of the vector s include cross-talk noise from the other sub-stream elements.
As predicted by Matrix Perturbation Theory (e.g. [7]), the achieved cross-talk SNR depends on the norm of the perturbation dH, which in our case depends on the channel measurements SNR and the number of measurements, as well as on certain relationships between the singular values of H, which are random in our case since the matrix H is assumed to be random.
In the context of the present invention it is also assumed that the Channel Matrix is relatively time invariant, that is only negligible changes in the matrix H occur during the duration of a transmission burst. This last assumption is reasonable when the relative motion between the communication devices is slow, such as in WLAN and Fixed Wireless Access Networks, or when the transmission bursts are of short duration (relative to the Doppler period), as is usually the case in Cellular Networks.